# Gustav A. Hedlund

**Gustav HedlundG. A. HedlundHedlund, Gustav A.**

Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American mathematician, was one of the founders of symbolic and topological dynamics.wikipedia

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### Symbolic dynamics

**symbolicCategorical dynamicsdynamic**

Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American mathematician, was one of the founders of symbolic and topological dynamics.

Related work was done by Emil Artin in 1924 (for the system now called Artin billiard), Pekka Myrberg, Paul Koebe, Jakob Nielsen, G. A. Hedlund.

### Marston Morse

**H. C. Marston MorseH. Marston MorseHarold Calvin Marston Morse**

He was a student of Marston Morse, under whose supervision he received a Ph.D. in 1930 with thesis entitled "I. Geodesics on a Two-Dimensional Riemannian Manifold with Periodic Coefficients II. Poincare's Rotation Number and Morse's Type Number".

### Topological dynamics

**topological dynamical systemtopological dynamical systemstopological methods**

Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American mathematician, was one of the founders of symbolic and topological dynamics.

### Walter Gottschalk

**Gottschalk, Walter**

He has over 200 academic descendants, many of them through two of his students at Virginia, Walter Gottschalk and W. Roy Utz, Jr.

Gottschalk did both his undergraduate studies and graduate studies at the University of Virginia, finishing with a Ph.D. in 1944 under the supervision of Gustav A. Hedlund.

### Curtis–Hedlund–Lyndon theorem

**translation-invariant and continuous**

The Curtis–Hedlund–Lyndon theorem, a topological characterization of cellular automata, is named after Hedlund.

It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund credited Curtis and Lyndon as co-discoverers.

### Cellular automaton

**cellular automataCACell games (cellular automaton)**

The Curtis–Hedlund–Lyndon theorem, a topological characterization of cellular automata, is named after Hedlund.

In 1969, Gustav A. Hedlund compiled many results following this point of view in what is still considered as a seminal paper for the mathematical study of cellular automata.

### Roger Lyndon

**Roger C. LyndonR. C. LyndonLyndon**

Hedlund first published this theorem in 1969, crediting Morton L. Curtis and Roger Lyndon as co-discoverers.

Lyndon was credited by Gustav A. Hedlund for his role in the discovery of the Curtis–Hedlund–Lyndon theorem, a mathematical characterization of cellular automata in terms of continuous equivariant functions on shift spaces.

### Morton L. Curtis

**Curtis, Morton L.M. L. Curtis**

Hedlund first published this theorem in 1969, crediting Morton L. Curtis and Roger Lyndon as co-discoverers.

Together with Gustav A. Hedlund and Roger Lyndon, he proved the Curtis–Hedlund–Lyndon theorem characterizing cellular automata as being defined by continuous equivariant functions on a shift space.

### Mathematician

**mathematiciansapplied mathematicianMathematics**

Gustav Arnold Hedlund (May 7, 1904 – March 15, 1993), an American mathematician, was one of the founders of symbolic and topological dynamics.

### Somerville, Massachusetts

**SomervilleSomerville, MAWest Somerville, Massachusetts**

Hedlund was born May 7, 1904, in Somerville, Massachusetts.

### Harvard University

**HarvardHarvard CollegeUniversity of Harvard**

He did his undergraduate studies at Harvard University, earned a master's degree from Columbia University, and returned to Harvard for his doctoral studies.

### Columbia University

**ColumbiaColumbia CollegeUniversity of Columbia**

He did his undergraduate studies at Harvard University, earned a master's degree from Columbia University, and returned to Harvard for his doctoral studies.

### Hunter College

**Hunter College of the City University of New YorkCUNY Hunter CollegeHunter**

While still studying at Columbia, Hedlund taught at Hunter College, and after receiving his doctorate he took a position at Bryn Mawr College, where he remained for nine years.

### Bryn Mawr College

**Bryn MawrBryn Mawr College LibraryBryn Mawr Alumnae Association**

While still studying at Columbia, Hedlund taught at Hunter College, and after receiving his doctorate he took a position at Bryn Mawr College, where he remained for nine years.

### University of Virginia

**VirginiaUniversity of Virginia at CharlottesvilleThe University of Virginia**

From 1939 to 1948 he taught at the University of Virginia, after which he moved to Yale University.

### Yale University

**YaleYale CollegeUniversity of Yale**

From 1939 to 1948 he taught at the University of Virginia, after which he moved to Yale University.

### Institute for Advanced Study

**Institute for Advanced StudiesInstitute for Advanced Study, PrincetonIAS**

He was also a member of the Institute for Advanced Study in Princeton, New Jersey, which he visited in 1933, 1938, and 1953.

### Princeton, New Jersey

**PrincetonPrinceton, NJPrinceton, N.J.**

He was also a member of the Institute for Advanced Study in Princeton, New Jersey, which he visited in 1933, 1938, and 1953.

### Wesleyan University

**WesleyanDavison Art CenterCollege of Social Studies**

He retired from Yale in 1972, but afterwards held a visiting professorship at Wesleyan University.

### Academic genealogy

**academic descendantsscientific genealogyacademic ancestor**

He has over 200 academic descendants, many of them through two of his students at Virginia, Walter Gottschalk and W. Roy Utz, Jr.

### Ergodicity

**ergodicergodic measurenon-ergodic**

One of Hedlund's early results was an important theorem about the ergodicity of geodesic flows.

### Geodesic

**geodesicsgeodesic flowgeodesic equation**

One of Hedlund's early results was an important theorem about the ergodicity of geodesic flows.

### Sigma Xi

**Scientific Research Society of AmericaSigma Xi SocietySigma Xi, The Scientific Research Society**

Hedlund was elected to Sigma Xi in 1943.

### Festschrift

**FestschriftenGedenkschriftliber amicorum**

The editor of the festschrift from the conference, Anatole Beck, wrote that it was "our token of respect to the man who did so much to foster and build this field".

### Anatole Beck

**Beck, Anatole**

The editor of the festschrift from the conference, Anatole Beck, wrote that it was "our token of respect to the man who did so much to foster and build this field".